Microbial contamination of food and alimentary toxoinfection/intoxication in humans are commonly caused by bacteria such as Salmonella spp., Escherichia coli, Yersinia spp., Campylobacter spp., Listeria monocytogenes, and fungi (Aspergillus, Fusarium). The addition of probiotic cultures (bacterial strains Lactobacillus and Bifidobacterium and the yeast Saccharomyces cerevisiae var. boulardii) to food contributes primarily to food enrichment and obtaining a functional product, but also to food preservation. Reducing the number of viable pathogenic microorganisms and eliminating or neutralizing their toxins in food is achieved by probiotic-produced antimicrobial substances such as organic acids (lactic acid, acetic acid, propionic acid, phenylacetic acid, and phenyllactic acid), fatty acids (linoleic acid, butyric acid, caproic acid, and caprylic acid), aromatic compounds (diacetyl, acetaldehyde, reuterin), hydrogen peroxide, cyclic dipeptides, bacteriocins, and salivabactin. This review summarizes the basic facts on microbial contamination and preservation of food and the potential of different probiotic strains and their metabolites (postbiotics), including the mechanisms of their antimicrobial action against various foodborne pathogens. Literature data on this topic over the last three decades was searched in the PubMed, Scopus, and Google Scholar databases, systematically presented, and critically discussed, with particular attention to the advantages and disadvantages of using probiotics and postbiotics as food biopreservatives.